Nonuniversality in helical and canted-spin systems

Azaria, P.; Delamotte, Bertrand; Jolicœur, Thierry

doi:10.1103/physrevlett.64.3175

Cited by 178 publications

(240 citation statements)

References 27 publications

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“…The application of this method to the noncollinear transition was first made by Azaria, Delamotte and Jolicoeur for the Heisenberg spins (n = 3) [31]. Extension to general n-component spins was made by Azaria, Delamotte, Delduc and Jolicoeur [32], and by the present author [80].…”

Section: Possible Tricritical Behaviorsmentioning

confidence: 99%

“…More specifically, mean-field tricritical behavior was invoked in those works [31,32,36]. It should be noticed, however, that the tricriticality in general is not necessarily mean-field tricritical, particular when the LGW Hamiltonian has more than one quartic coupling as in our model [79].…”

Section: Possible Tricritical Behaviorsmentioning

confidence: 99%

“…By contrast, a more conservative view was proposed by Azaria, Delamotte and Jolicoeur a few years later [31,32]. These authors studied a certain nonlinear sigma model expected to describe the Heisenberg (n = 3) noncollinear or canted magnets based on the RG ǫ = d−2 expansion technique, and found a stable fixed point which was nothing but the standard O(4) Wilson-Fisher fixed point.…”

Section: (B) Chiralitymentioning

confidence: 99%

“…As mentioned, in the Heisenberg (n = 3) case, ǫ = d−2 expansion predicts that the symmetry is dynamically restored, yielding the standard O(4) critical behavior which has never been seen in the ǫ = 4 − d expansion. Based on this observation, Azaria et al claimed that the (n = 3, d = 3) noncollinear transition should be of standard O(4) universality [31,32]. They further speculated that the transition could also be first order or mean-field tricritical, depending on the microscopic parameters of the system.…”

Section: Fixed Points and Exponentsmentioning

confidence: 99%

“…In the limit n → 2, the fixed-point temperature tends to infinity and the ǫ = d − 2 expansion becomes meaningless. Azaria et al observed that, in the particular case of Heisenberg spins (n = 3), the obtained fixed point was nothing but the standard O(4) Wilson-Fisher fixed point [31]. Note that this O(4) fixed point is different in nature from the O(4)-like fixed point obtained by Bak and Mukamel in the ǫ = 4 − d expansion analysis of the XY (n = 2) noncollinear magnets: The former fixed point has no counterpart in the ǫ = 4 − d expansion [4].…”

Section: Fixed Points and Exponentsmentioning

confidence: 99%

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Kawamura¹

1998

J. Phys.: Condens. Matter

340

470

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Recent theoretical and experimental studies on the critical properties of frustrated antiferromagnets with the noncollinear spin order, including stacked-triangular antiferromagnets and helimagnets, are reviewed. Particular emphasis is put on the novel critical and multicritical behaviors exhibited by these magnets, together with an important role played by the 'chirality'. §1. Introduction Phase transitions and critical phenomena have been a central issue of statistical physics for many years. In particular, phase transitions of magnets or of 'spin systems' have attracted special interest. Thanks to extensive theoretical and experimental studies, we now have rather good understanding of the nature of phase transitions of standard ferromagnets and antiferromagnets. By the term 'standard', I mean here regular and unfrustrated magnets without quenched disorder and frustration. They include ferromagnets and unfrustrated antiferromagnets with the collinear spin order.One key notion which emerged through these studies is the notion of universality. According to the universality hypothesis, a variety of continuous (or secondorder) phase transitions can be classified into a small number of universality classes determined by a few basic properties characterizing the system under study, such as the space dimensionality d, the symmetry of the order parameter and the range of interaction. If one is interested only in the so-called universal quantities, such as critical exponents, amplitude ratios and scaled equation of state, various phase transitions should exhibit exactly the same behavior. In the case of standard bulk magnets in three spatial dimensions (d = 3), universality class is basically determined by the number of the spin components, n. Physically, the index n is related to the type of magnetic anisotropy: Namely, n = 1 (Ising), n = 2 (XY ) and n = 3 (Heisenberg) correspond to magnets with easy-axis-type anisotropy, easy-plane-type anisotropy and no anisotropy (isotropic magnets), respectively. The critical properties associated with these n-component O(n) universality classes have been extensively studied and are now rather well understood. From the renormalization-group (RG) viewpoint, these critical properties are governed by the so-called Wilson-Fisher O(n) fixed point.

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Section: Possible Tricritical Behaviorsmentioning

confidence: 99%

Section: Possible Tricritical Behaviorsmentioning

confidence: 99%

Section: (B) Chiralitymentioning

confidence: 99%

Section: Fixed Points and Exponentsmentioning

confidence: 99%

Section: Fixed Points and Exponentsmentioning

confidence: 99%

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Kawamura¹

1998

J. Phys.: Condens. Matter

340

470

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ChemInform Abstract: Spin and Chirality Orderings of Frustrated Magnets. Stacked‐Triangular Antiferromagnets and Spin Glasses.

Kawamura

2002

ChemInform

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Quantum Phase Transitions of Antiferromagnets and the Cuprate Superconductors

Sachdev

2012

Modern Theories of Many-Particle Systems in Condensed Matter Physics

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I begin with a proposed global phase diagram of the cuprate superconductors as a function of carrier concentration, magnetic field, and temperature, and highlight its connection to numerous recent experiments. The phase diagram is then used as a point of departure for a pedagogical review of various quantum phases and phase transitions of insulators, superconductors, and metals. The bond operator method is used to describe the transition of dimerized antiferromagnetic insulators between magnetically ordered states and spin-gap states. The Schwinger boson method is applied to frustrated square lattice antiferromagnets: phase diagrams containing collinear and spirally ordered magnetic states, Z 2 spin liquids, and valence bond solids are presented, and described by an effective gauge theory of spinons. Insights from these theories of insulators are then applied to a variety of symmetry breaking transitions in d-wave superconductors. The latter systems also contain fermionic quasiparticles with a massless Dirac spectrum, and their influence on the order parameter fluctuations and quantum criticality is carefully discussed. I conclude with an introduction to strong coupling problems associated with symmetry breaking transitions in two-dimensional metals, where the order parameter fluctuations couple to a gapless line of fermionic excitations along the Fermi surface.

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Nonuniversality in helical and canted-spin systems

Cited by 178 publications

References 27 publications

Untitled

Untitled

ChemInform Abstract: Spin and Chirality Orderings of Frustrated Magnets. Stacked‐Triangular Antiferromagnets and Spin Glasses.

Quantum Phase Transitions of Antiferromagnets and the Cuprate Superconductors

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